Social and industrial networks frequently demonstrate a core-periphery structure where the set of nodes can be partitioned into a clique (“core”) and an empty network (“periphery”). A possible explanation for the formation of this structure is provided by introducing type heterogeneity into the basic connections model. A two-type society is “power based” if for any given path length, both types prefer to connect to the “superior” type over the “inferior” type. Core-periphery networks, in which the “superior” agents are in the core and the “inferior” agents are in the periphery, emerge as a dominant architecture (pairwise stable and strongly efficient) in a “power based” society as long as the linking costs are intermediate. Thus, in this framework, the network formation process converts an exogenous, intellectual advantage into a central position in the network.